According to @BobTheChicken, it's against Apple's terms of use play music videos. However, there are a few apps that use their own custom video player (or find other ways to stream YT videos remotely), and they have not been taken down by Apple. Here is an example: https://itunes.apple.com/us/app/music-tubee-free-music-player/id607974779?mt=8
@shalins, any chance you can look into this as well?